3B · Chapter 11 · Lesson 1
Meters and Centimeters
Represent meters and centimeters and rename lengths in mixed units.
Today's mathematical question
Convert 5 m 40 cm into cm.
Learning target
Represent meters and centimeters and rename lengths in mixed units.
Before starting: Grade 3A: place value and subtraction. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
How many hundreds are in 500?
Reveal explanation
Answer: 5
Five hundred is five complete groups of one hundred: 100 + 100 + 100 + 100 + 100 = 500. Changing the unit does not change the quantity.
- P2
Find 1,200 − 300.
Reveal explanation
Answer: 900
Twelve hundreds minus three hundreds is nine hundreds.
- P3
Write 1,000 + 35 in standard form.
Reveal explanation
Answer: 1,035
One thousand plus three tens and five ones gives 1,035. The zero in the hundreds place means there are no additional hundreds.
Learn and understand
A meter contains 100 centimeters. One meter and 35 centimeters therefore means 100 + 35 = 135 centimeters. Converting units changes the way the length is written, not the length itself. Keep the unit attached to every answer so the number is meaningful. A meter has 100 centimeters. For 2 m 35 cm, count two bundles of 100 cm plus 35 cm, giving 235 cm. Record the output unit carefully.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Use a meter strip divided into 100 centimeter units. Combine full meters and leftover centimeters before renaming.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- meter
- metric unit of length equal to 100 cm
- centimeter
- one hundredth of a meter
- mixed units
- full large units and leftover small units
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Convert 5 m 40 cm into cm.
- Identify the whole, the units, and what the question asks.
- 5 m = 500 cm; add 40 to make 540 cm.
- Check that the answer uses the right units and makes sense.
Answer: 540 cm
Check your understanding 1
Convert 3 m 25 cm into cm.
Reveal answer and explanation
325 cm — 3 m = 300 cm; add 25 to make 325 cm.
Worked example 2
Explore, calculate, verify
Express 350 cm as m and cm.
- Identify the whole, the units, and what the question asks.
- Partition 350 into 3 full groups of 100 plus 50.
- Check that the answer uses the right units and makes sense.
Answer: 3 m 50 cm
Check your understanding 2
Express 550 cm as m and cm.
Reveal answer and explanation
5 m 50 cm — Partition 550 into 5 full groups of 100 plus 50.
Worked example 3
Explore, calculate, verify
Convert 8 m 50 cm into cm.
- Identify the whole, the units, and what the question asks.
- 8 m = 800 cm; add 50 to make 850 cm.
- Check that the answer uses the right units and makes sense.
Answer: 850 cm
Check your understanding 3
Express 580 cm as m and cm.
Reveal answer and explanation
5 m 80 cm — Partition 580 into 5 full groups of 100 plus 80.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
Convert 7 m 40 cm into cm.
Reveal explanation
Answer: 740 cm
7 m = 700 cm; add 40 to make 740 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - G2
Express 640 cm as m and cm.
Reveal explanation
Answer: 6 m 40 cm
Partition 640 into 6 full groups of 100 plus 40.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - G3
Convert 7 m 75 cm into cm.
Reveal explanation
Answer: 775 cm
7 m = 700 cm; add 75 to make 775 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - G4
Express 340 cm as m and cm.
Reveal explanation
Answer: 3 m 40 cm
Partition 340 into 3 full groups of 100 plus 40.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - G5
Convert 5 m 50 cm into cm.
Reveal explanation
Answer: 550 cm
5 m = 500 cm; add 50 to make 550 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
Convert 6 m 75 cm into cm.
Reveal explanation
Answer: 675 cm
6 m = 600 cm; add 75 to make 675 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - I2
Express 455 cm as m and cm.
Reveal explanation
Answer: 4 m 55 cm
Partition 455 into 4 full groups of 100 plus 55.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - I3
Convert 3 m 50 cm into cm.
Reveal explanation
Answer: 350 cm
3 m = 300 cm; add 50 to make 350 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - I4
Express 620 cm as m and cm.
Reveal explanation
Answer: 6 m 20 cm
Partition 620 into 6 full groups of 100 plus 20.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - I5
Express 575 cm as m and cm.
Reveal explanation
Answer: 5 m 75 cm
Partition 575 into 5 full groups of 100 plus 75.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - I6
Convert 6 m 20 cm into cm.
Reveal explanation
Answer: 620 cm
6 m = 600 cm; add 20 to make 620 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - I7
Express 265 cm as m and cm.
Reveal explanation
Answer: 2 m 65 cm
Partition 265 into 2 full groups of 100 plus 65.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - I8
Convert 4 m 75 cm into cm.
Reveal explanation
Answer: 475 cm
4 m = 400 cm; add 75 to make 475 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
A student claims 6 m 40 cm means 640 m. What unit should the total use?
Reveal explanation
Answer: 640 cm
There are 100 centimeters in one meter, so 6 m 40 cm equals 640 cm, not meters.
- C2
Explain how to subtract 70 cm from 6 m 20 cm without writing a negative number of centimeters.
Reveal explanation
Answer: 5 m 50 cm
Exchange 1 m for 100 cm: 5 m 120 cm − 70 cm = 5 m 50 cm.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
Convert 6 m 80 cm into cm.
Reveal explanation
Answer: 680 cm
6 m = 600 cm; add 80 to make 680 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - E2
Convert 4 m 25 cm into cm.
Reveal explanation
Answer: 425 cm
4 m = 400 cm; add 25 to make 425 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity. - E3
Convert 8 m 20 cm into cm.
Reveal explanation
Answer: 820 cm
8 m = 800 cm; add 20 to make 820 cm.
One larger unit is exchanged into an equal number of smaller units without changing the quantity.